The term machine learning refers to a toolbox of methods which are able to extract information from a possibly huge amount of data and which have been applied extremely successfully in the last (few) decades. Due to the large datasets that have to be handled, their efficient implementation and application comes with computational and algorithmic challenges. Hence, many important aspects of machine learning are at the heart of computer science. On the other hand the methodological foundation of machine learning builds on mathematical disciplines, in particular, statistics, optimisation and approximation theory. In this lecture we will give a mathematical answer to the question: How and why do machine learning methods work? More precisely, we aim for a rigorous and mathematical analysis of some of these celebrated methods. Our focus is on statistical aspects.